1. Geol 4068 Class presentation to accompany reading of Chapter 2- Waves in Fluids Elements of 3D Seismology, 2nd Edition by Christopher Liner September 6, 2005 Juan M. Lorenzo

2. Outline What is a Fluid? Elastic Moduli Acoustic Solution to the Wave equation Density Velocity

3. Outline What is a Fluid? Elastic Moduli Acoustic Solution to the Wave equation Density Velocity

4. Fluid (no shear strength) Porous solid (Solid+fluid - BIOT THEORY) Solid (shear strength and high and finite resistance to compressibility TYPES OF SEISMIC MATERIALS

5. Outline What is a Fluid? Elastic Moduli Acoustic Solution to the Wave equation Density Velocity

6. Key Physical Parameters of the Acoustic Wave Equation (Pa) Bulk Modulus or modulus of incompressibility

7. Key Physical Parameters of the Acoustic Wave Equation (Pa) Bulk Modulus or modulus of incompressibility

8. Example: Ocean Water density = 1,035 kg.m^3 Incompressibility modulus is of order 10^9 Pa

9. Outline What is a Fluid? Elastic Moduli Acoustic Solution to the Wave equation Density Velocity

10. Different Approaches Hooke’s Law: stress (Pa)= Y (Pa). strain + Newton’s Law (F=ma) Lagrangian Mechanics (Energy Relationships)

11. Outline What is a Fluid? Elastic Moduli Acoustic Solution to the Wave equation Density Velocity

12. Density is given minor importance with respect to velocity. Usually velocity and denisty increase together. Gardner’s Rule (Gardner et a., 1974) density = a.V^0.25, where a=0.31 Salt: 4500-5000 m/s; 2.0-2.1 g/cc

13. Outline What is a Fluid? Elastic Moduli Acoustic Solution to the Wave equation Density Velocity

14. (… geometric mean)

15. Very important for basic seismic processing. Can be obtained directly from seismic field data or GPR field data. Errors ~10% Mean velocity; traditional

16. V=330 m/s, rho =0 z=100000m s = 200m; V=1000 m/s, rho =1.6 V=1500 m/s, z= 500m rho =1.8 i=1 i=2 i=3=j

17. Excel macro